A theoretical model of jump diffusion-mean reversion: Constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor

Abstract

Purpose

The purpose of this paper is to develop a theoretical model of a jump diffusion-mean reversion constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor as opposed to the deterministic floor used in the previous literatures.

Design/methodology/approach

The paper adopts Merton’s jump diffusion (JD) model to simulate the price path followed by risky assets and the CIR mean reversion model to simulate the path followed by the short-term interest rate. The floor of the CPPI strategy is linked to the stochastic process driving the value of a fixed income instrument whose yield follows the CIR mean reversion model. The developed model is benchmarked against CNX-NIFTY 50 and is back tested during the extreme regimes in the Indian market using the scenario-based Monte Carlo simulation technique.

Findings

Back testing the algorithm using Monte Carlo simulation across the crisis and recovery phases of the 2008 recession regime revealed that the portfolio performs better than the risky markets during the crisis by hedging the downside risk effectively and performs better than the fixed income instruments during the growth phase by leveraging on the upside potential. This makes it a value-enhancing proposition for the risk-averse investors.

Originality/value

The study modifies the CPPI algorithm by re-defining the floor of the algorithm to be a stochastic mean reverting process which is guided by the movement of the short-term interest rate in the economy. This development is more relevant for two reasons: first, the short-term interest rate changes with time, and hence the constant yield during each rebalancing steps is not practically feasible; second, the historical literatures have revealed that the short-term interest rate tends to move opposite to that of the equity market. Thereby, during the bear run the floor will increase at a higher rate, whereas the growth of the floor will stagnate during the bull phase which aids the model to capitalize on the upward potential during the growth phase and to cut down on the exposure during the crisis phase.

Citation

Chakrabarty, A., Luo, Z., Dubey, R. and Jiang, S. (2017), "A theoretical model of jump diffusion-mean reversion: Constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor", Business Process Management Journal, Vol. 23 No. 3, pp. 537-554. https://doi.org/10.1108/BPMJ-01-2016-0005